robinhouston · July 28, 2013 14:16
diff --git a/index.html b/index.html
 <!DOCTYPE html>
 <meta charset="utf-8">
 <title>Double stumbling blocks</title>
 <script src="http://bl.ocks.org/robinhouston/raw/6096562/rAF.js" charset="utf-8"></script>
 <script src="http://bl.ocks.org/robinhouston/raw/6096562/doyle.js" charset="utf-8"></script>
 <canvas width=960 height=500></canvas>
 <script>
    // Initialisation
    var canvas = document.getElementsByTagName("canvas")[0],
        context = canvas.getContext("2d");
    
    
    // Complex arithmetic
    function cmul(w, z) {
        return [
            w[0]*z[0] - w[1]*z[1],
            w[0]*z[1] + w[1]*z[0]
        ];
    }
    function csub(w, z) {
        return [ w[0]-z[0], w[1]-z[1] ];
    }
    function modulus(p) {
        return Math.sqrt(p[0]*p[0] + p[1]*p[1]);
    }
    function crecip(z) {
        var d = z[0]*z[0] + z[1]*z[1];
        return [z[0]/d, -z[1]/d];
    }
    function cpow(z, n) {
        var mod = Math.pow(modulus(z), n), arg = Math.atan2(z[1], z[0]) * n;
        return [ mod*Math.cos(arg), mod*Math.sin(arg) ];
    }
    
    // Möbius transformation that maps (0, 1, ∞) to (-1, 0, 1)
    function transform_point(p) {
        var x = p[0], y = p[1];
        var denom = (x+1)*(x+1) + y*y;
        return [ (x*x - 1 + y*y)/denom, 2*y/denom ];
    }
    
    // Doyle spiral drawing
    function spiral(r, start_point, delta, gamma, options) {
        var recip_delta = crecip(delta),
            mod_delta = modulus(delta),
            mod_recip_delta = 1/mod_delta,
            color_index = options.i,
            colors = options.fill,
            min_d = options.min_d,
            max_d = options.max_d,
            delta_gamma = cmul(delta, gamma),
            delta_over_gamma = cmul(delta, crecip(gamma)),
            gamma_over_delta = cmul(gamma, crecip(delta));
        
        // Spiral inwards
        for (var q = start_point, mod_q = modulus(q);
            mod_q > min_d;
            q = cmul(q, recip_delta), mod_q *= mod_recip_delta
        ) {
            color_index = (color_index + colors.length - 1) % colors.length;
        }
        
        // Spiral outwards
        for (;mod_q < max_d; q = cmul(q, delta), mod_q *= mod_delta, color_index = (color_index + 1) % colors.length) {
            var quad = [transform_point(q)];
            if (modulus(quad[0]) > 10) continue;

            if (color_index == 0)
                quad.push(transform_point(cmul(q, delta_over_gamma)));
            quad.push(transform_point(cmul(q, delta)));
            if (color_index == 2)
                quad.push(transform_point(cmul(q, delta_gamma)));
            quad.push(transform_point(cmul(q, gamma)));
            if (color_index == 1)
                quad.push(transform_point(cmul(q, gamma_over_delta)));
            
            if (modulus(csub(quad[0], quad[2])) > 5) continue;
            
            context.fillStyle = colors[color_index];
            context.beginPath();
            context.moveTo(quad[0][0], quad[0][1]);
            context.lineTo(quad[1][0], quad[1][1]);
            context.lineTo(quad[2][0], quad[2][1]);
            context.lineTo(quad[3][0], quad[3][1]);
            context.closePath();
            context.fill();
        }
    }
    
    
    // Animation
    var p = 9, q = 24;
    var root = doyle(p, q);
    
    var ms_per_repeat = 750;
    
    function frame(t) {
        context.setTransform(1, 0, 0, 1, 0, 0);
        context.clearRect(0, 0, canvas.width, canvas.height);
        
        context.translate(Math.round(canvas.width/2), cy = Math.round(canvas.height/2));
        context.scale(200, 200);
        context.rotate(Math.PI / 12);
        
        var min_d = 1e-3, max_d = 1e3;
        var start = cpow(root.a, t);
        for (var i=0; i<q; i++) {
            spiral(root.r, start, root.a, root.b, {
                fill: ["#050505", "#D2D2D2", "#676767"], i: (2*i)%3,
                min_d: min_d, max_d: max_d
            });
            start = cmul(start, root.b);
        }
    }
    
    var first_timestamp;
    function loop(timestamp) {
        if (!first_timestamp) first_timestamp = timestamp;
        frame(((timestamp - first_timestamp) % (3*ms_per_repeat)) / ms_per_repeat);
        requestAnimationFrame(loop);
    }
    
    requestAnimationFrame(loop);
 </script>
	<!DOCTYPE html>
	<meta charset="utf-8">
	<title>Double stumbling blocks</title>
	<script src="http://bl.ocks.org/robinhouston/raw/6096562/rAF.js" charset="utf-8"></script>
	<script src="http://bl.ocks.org/robinhouston/raw/6096562/doyle.js" charset="utf-8"></script>
	<canvas width=960 height=500></canvas>
	<script>
	// Initialisation
	var canvas = document.getElementsByTagName("canvas")[0],
	context = canvas.getContext("2d");


	// Complex arithmetic
	function cmul(w, z) {
	return [
	w[0]z[0] - w[1]z[1],
	w[0]z[1] + w[1]z[0]
	];
	}
	function csub(w, z) {
	return [ w[0]-z[0], w[1]-z[1] ];
	}
	function modulus(p) {
	return Math.sqrt(p[0]p[0] + p[1]p[1]);
	}
	function crecip(z) {
	var d = z[0]z[0] + z[1]z[1];
	return [z[0]/d, -z[1]/d];
	}
	function cpow(z, n) {
	var mod = Math.pow(modulus(z), n), arg = Math.atan2(z[1], z[0]) * n;
	return [ modMath.cos(arg), modMath.sin(arg) ];
	}

	// Möbius transformation that maps (0, 1, ∞) to (-1, 0, 1)
	function transform_point(p) {
	var x = p[0], y = p[1];
	var denom = (x+1)(x+1) + yy;
	return [ (xx - 1 + yy)/denom, 2*y/denom ];
	}

	// Doyle spiral drawing
	function spiral(r, start_point, delta, gamma, options) {
	var recip_delta = crecip(delta),
	mod_delta = modulus(delta),
	mod_recip_delta = 1/mod_delta,
	color_index = options.i,
	colors = options.fill,
	min_d = options.min_d,
	max_d = options.max_d,
	delta_gamma = cmul(delta, gamma),
	delta_over_gamma = cmul(delta, crecip(gamma)),
	gamma_over_delta = cmul(gamma, crecip(delta));

	// Spiral inwards
	for (var q = start_point, mod_q = modulus(q);
	mod_q > min_d;
	q = cmul(q, recip_delta), mod_q *= mod_recip_delta
	) {
	color_index = (color_index + colors.length - 1) % colors.length;
	}

	// Spiral outwards
	for (;mod_q < max_d; q = cmul(q, delta), mod_q *= mod_delta, color_index = (color_index + 1) % colors.length) {
	var quad = [transform_point(q)];
	if (modulus(quad[0]) > 10) continue;

	if (color_index == 0)
	quad.push(transform_point(cmul(q, delta_over_gamma)));
	quad.push(transform_point(cmul(q, delta)));
	if (color_index == 2)
	quad.push(transform_point(cmul(q, delta_gamma)));
	quad.push(transform_point(cmul(q, gamma)));
	if (color_index == 1)
	quad.push(transform_point(cmul(q, gamma_over_delta)));

	if (modulus(csub(quad[0], quad[2])) > 5) continue;

	context.fillStyle = colors[color_index];
	context.beginPath();
	context.moveTo(quad[0][0], quad[0][1]);
	context.lineTo(quad[1][0], quad[1][1]);
	context.lineTo(quad[2][0], quad[2][1]);
	context.lineTo(quad[3][0], quad[3][1]);
	context.closePath();
	context.fill();
	}
	}


	// Animation
	var p = 9, q = 24;
	var root = doyle(p, q);

	var ms_per_repeat = 750;

	function frame(t) {
	context.setTransform(1, 0, 0, 1, 0, 0);
	context.clearRect(0, 0, canvas.width, canvas.height);

	context.translate(Math.round(canvas.width/2), cy = Math.round(canvas.height/2));
	context.scale(200, 200);
	context.rotate(Math.PI / 12);

	var min_d = 1e-3, max_d = 1e3;
	var start = cpow(root.a, t);
	for (var i=0; i<q; i++) {
	spiral(root.r, start, root.a, root.b, {
	fill: ["#050505", "#D2D2D2", "#676767"], i: (2*i)%3,
	min_d: min_d, max_d: max_d
	});
	start = cmul(start, root.b);
	}
	}

	var first_timestamp;
	function loop(timestamp) {
	if (!first_timestamp) first_timestamp = timestamp;
	frame(((timestamp - first_timestamp) % (3*ms_per_repeat)) / ms_per_repeat);
	requestAnimationFrame(loop);
	}

	requestAnimationFrame(loop);
	</script>